We present the results of experiments studying the shape of craters formed by the normal impact of a solid spherical projectile into a deep noncohesive granular bed at low energies. The resultant impact crater surfaces are accurately digitized using laser profilometry, allowing for the detailed investigation of the crater shape. We find that these impact craters are very nearly hyperbolic in profile. Crater radii and depths are dependent on impact energy, as well as the projectile density and size. The precise crater shape is a function of the crater aspect ratio. While the dimensions of the crater are highly dependent on the impact energy, we show that the energy required to excavate the crater is only a tiny fraction (0.1%-0.5%) of the kinetic energy of the projectile.

We study the behavior of a yield-stress fluid following the impact of a vertically falling sphere. Since the impact produces shear stresses larger than the yield stress, the material in the vicinity of the impact becomes fluidized. The sphere entrains air when it enters the fluid, and the resulting cavity pinches off below the surface. The upper part of this cavity then rebounds upward. For sufficiently fast impacts, a vertical jet is produced by the cavity collapse. While many aspects of this process are similar to that in Newtonian fluids or granular materials, the rheological properties of our target material change the scaling of the cavity pinch-off depth and have a dramatic effect on the height of the jets. The material returns to a solid-like behavior once the stresses due to the impact have relaxed to below the yield stress, leaving a crater in the surface of the material. We find that the diameter of this crater depends nonmonotonically on the impact speed. The crater shape also changes with speed, reflecting the dynamics of the impact process.

We report on an experimental and numerical study of the collapse under gravity of a rectangular well in a quasi-two-dimensional granular bed. For comparison, we also perform experiments on the collapse of a single vertical step. Experiments are conducted in a vertical Hele-Shaw cell, which allows the flow to be recorded from the side using high-speed video. If the rectangular well is sufficiently narrow, the collapsing sidewalls collide at the center of the well and the dynamics of the collapse are dependant on the aspect ratio of the initial well. We follow the evolution of the free surface from the video images, and use particle image velocimetry to determine the subsurface velocity field. From these data, the potential and kinetic energy of the system are calculated. We observe two stages to the collapse flow: an initial gravity-dominated stage, during which the kinetic energy increases, and a later dissipation-dominated phase during which the kinetic energy decreases. We find that although both the width and depth of the depression that remains after the well has collapsed depend on the initial aspect ratio, the surface profiles are self-similar; that is, the shape of the final profile is independent of the aspect ratio of the initial well. We model the collapse of the well using a depth-averaged continuum model with basal friction and with a discrete element model. Both models give results which agree well with experiment. The discrete element model indicates that friction between the particles is the most important source of dissipation over the course of the collapse.